Seminars & Colloquia Calendar

Download as iCal file

Nonlinear Analysis

Total Curvature and the isoperimetric inequality in negatively curved manifolds

Joel Spruck, Johns Hopkins University

Location:  Hill 705
Date & time: Tuesday, 22 October 2019 at 1:40PM - 2:50PM

Abstract: We prove that the total positive Gauss-Kronecker curvature of any closed hypersurface embedded in a complete simply connected manifold of nonpositive curvature \(Mn,\,n\geq 2\), is bounded below by the volume of the unit sphere in Euclidean space \(R^n\).

This yields the optimal isoperimetric inequality for bounded regions of finite perimeter in \(M\), and thus settles the Cartan-Hadamard conjecture. Our starting point is a comparison formula for total curvature of level sets in Riemannian manifolds.

This is joint work with Mohammad Ghomi.

Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.